I've heard it claimed that Satan was the worship leader for God's choir. I cannot find any scripture in the Bible that mentions Satan was in worship in heaven and was closest to God. What is the Biblical basis for this belief?
Based on Satan was a cherubim, then yes.
Cherubim/cherubs are angelic beings involved in the worship and praise of God.
Who is Satan?
Satan comes from Judaism; "Satan" is from the Hebrew word for "adversary." Satan was existed in the traditions of Judaism as the heavenly prosecutor in what Christians call the Old Testament long before the incarnation of the logos aka the birth of Jesus.
Job 1:6 NIV
One day the angels came to present themselves before the Lord, and Satan also came with them.
Satan's origins are hinted at here:
Ezekiel 28:16 NIV
Through your widespread trade you were filled with violence, and you sinned. So I drove you in disgrace from the mount of God, and I expelled you, guardian cherub, from among the fiery stones.
Power the cherubim
Isaiah 37:16 NIV
Lord Almighty, the God of Israel, enthroned between the cherubim, you alone are God over all the kingdoms of the earth. You have made heaven and earth.
Here is a popular depiction of the order from Matthaeus (Matthäus) Merian the elder (1593-1650).
Relationship to music
Ezekiel 28:13 hints to his relationship to music (see pipes and timbrels)
Ezekiel 28:13 KJV
Thou hast been in Eden the garden of God; every precious stone was thy covering, the sardius, topaz, and the diamond, the beryl, the onyx, and the jasper, the sapphire, the emerald, and the carbuncle, and gold: the workmanship of thy tabrets and of thy pipes was prepared in thee in the day that thou wast created.
This is entirely possible, as there are many allusions to the angels and saints in heaven engaging in a divine liturgy, particularly throughout Revelation. They are described as continually serving God in a variety of ways. This is based on the description of Lucifer as a cherubim, which are associated with the altar and the Ark in many passages, as well as the description of Lucifer as the fallen one in Isaiah 14.
It is also important to note that worship can also refer to more than music or praise only. The name Lucifer means "light-bearer", and this may very well refer to his specific role in the worship liturgy, rather than only a description of him in terms of personal attributes. As a similar example, in many liturgies practiced today there is a role of Thurifer, which describes the role of the incense bearer (it seems reasonable that a church might not want to call someone that brings candles or light the "Lucifer", given the associations with that name).